Taken together, the results presented above identify a near-term path to detect small H\(_2\)  atmospheres that can be consistent with liquid-water oceans on temperate exoplanets. H\(_2\)  atmospheres are probably the only type of temperate atmospheres readily within the reach of JWST and ARIEL for detailed studies, since to characterize a heavier H\(_2\) O, N\(_2\) , or CO\(_2\)  atmosphere will require co-adding a few tens transits – something not impossible but probably very hard [1]}, [2]}, [3]}, [4]}, [5]}. The mass of the H\(_2\)  atmospheres – a parameter that is not directly measured by transits but critical for habitability if the planet is moderately irradiated – can be inferred from transmission spectra via the signature gases that indicate solubility equilibria versus gas-phase thermochemical recycling. The biggest uncertainty is probably the temperature at the \(100\sim 1000\) -bar pressure level in the massive-atmosphere scenarios, which may be affected by ad hot heating mechanisms such as tidal heating. Detailed models of the interior temperature and mixing may further constrain this uncertainty [6]}, [7]}. Based on the range of the parameter space explored, we suggest that the sensitivity of multiple gases provided by future observatories' expanded wavelength coverage over Hubble would enable broad categorization of small versus massive atmospheres, summarized as a roadmap in Figure REF , panel b.
